Optimal. Leaf size=118 \[ -\frac{30375 (1-2 x)^{13/2}}{3328}+\frac{277425 (1-2 x)^{11/2}}{1408}-\frac{246315}{128} (1-2 x)^{9/2}+\frac{10121229}{896} (1-2 x)^{7/2}-\frac{2887773}{64} (1-2 x)^{5/2}+\frac{52725715}{384} (1-2 x)^{3/2}-\frac{60160485}{128} \sqrt{1-2 x}-\frac{39220335}{128 \sqrt{1-2 x}}+\frac{22370117}{768 (1-2 x)^{3/2}} \]
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Rubi [A] time = 0.0220235, antiderivative size = 118, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042, Rules used = {88} \[ -\frac{30375 (1-2 x)^{13/2}}{3328}+\frac{277425 (1-2 x)^{11/2}}{1408}-\frac{246315}{128} (1-2 x)^{9/2}+\frac{10121229}{896} (1-2 x)^{7/2}-\frac{2887773}{64} (1-2 x)^{5/2}+\frac{52725715}{384} (1-2 x)^{3/2}-\frac{60160485}{128} \sqrt{1-2 x}-\frac{39220335}{128 \sqrt{1-2 x}}+\frac{22370117}{768 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^5 (3+5 x)^3}{(1-2 x)^{5/2}} \, dx &=\int \left (\frac{22370117}{256 (1-2 x)^{5/2}}-\frac{39220335}{128 (1-2 x)^{3/2}}+\frac{60160485}{128 \sqrt{1-2 x}}-\frac{52725715}{128} \sqrt{1-2 x}+\frac{14438865}{64} (1-2 x)^{3/2}-\frac{10121229}{128} (1-2 x)^{5/2}+\frac{2216835}{128} (1-2 x)^{7/2}-\frac{277425}{128} (1-2 x)^{9/2}+\frac{30375}{256} (1-2 x)^{11/2}\right ) \, dx\\ &=\frac{22370117}{768 (1-2 x)^{3/2}}-\frac{39220335}{128 \sqrt{1-2 x}}-\frac{60160485}{128} \sqrt{1-2 x}+\frac{52725715}{384} (1-2 x)^{3/2}-\frac{2887773}{64} (1-2 x)^{5/2}+\frac{10121229}{896} (1-2 x)^{7/2}-\frac{246315}{128} (1-2 x)^{9/2}+\frac{277425 (1-2 x)^{11/2}}{1408}-\frac{30375 (1-2 x)^{13/2}}{3328}\\ \end{align*}
Mathematica [A] time = 0.0228421, size = 53, normalized size = 0.45 \[ -\frac{7016625 x^8+47670525 x^7+153878760 x^6+324478899 x^5+540496701 x^4+905206628 x^3+2892917004 x^2-5818266408 x+1938557272}{3003 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 50, normalized size = 0.4 \begin{align*} -{\frac{7016625\,{x}^{8}+47670525\,{x}^{7}+153878760\,{x}^{6}+324478899\,{x}^{5}+540496701\,{x}^{4}+905206628\,{x}^{3}+2892917004\,{x}^{2}-5818266408\,x+1938557272}{3003} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.89602, size = 105, normalized size = 0.89 \begin{align*} -\frac{30375}{3328} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} + \frac{277425}{1408} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{246315}{128} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{10121229}{896} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{2887773}{64} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{52725715}{384} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{60160485}{128} \, \sqrt{-2 \, x + 1} + \frac{290521 \,{\left (1620 \, x - 733\right )}}{768 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.69937, size = 243, normalized size = 2.06 \begin{align*} -\frac{{\left (7016625 \, x^{8} + 47670525 \, x^{7} + 153878760 \, x^{6} + 324478899 \, x^{5} + 540496701 \, x^{4} + 905206628 \, x^{3} + 2892917004 \, x^{2} - 5818266408 \, x + 1938557272\right )} \sqrt{-2 \, x + 1}}{3003 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 36.6611, size = 105, normalized size = 0.89 \begin{align*} - \frac{30375 \left (1 - 2 x\right )^{\frac{13}{2}}}{3328} + \frac{277425 \left (1 - 2 x\right )^{\frac{11}{2}}}{1408} - \frac{246315 \left (1 - 2 x\right )^{\frac{9}{2}}}{128} + \frac{10121229 \left (1 - 2 x\right )^{\frac{7}{2}}}{896} - \frac{2887773 \left (1 - 2 x\right )^{\frac{5}{2}}}{64} + \frac{52725715 \left (1 - 2 x\right )^{\frac{3}{2}}}{384} - \frac{60160485 \sqrt{1 - 2 x}}{128} - \frac{39220335}{128 \sqrt{1 - 2 x}} + \frac{22370117}{768 \left (1 - 2 x\right )^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.51704, size = 162, normalized size = 1.37 \begin{align*} -\frac{30375}{3328} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} - \frac{277425}{1408} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{246315}{128} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{10121229}{896} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{2887773}{64} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{52725715}{384} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{60160485}{128} \, \sqrt{-2 \, x + 1} - \frac{290521 \,{\left (1620 \, x - 733\right )}}{768 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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